1. Field of the Invention
The present invention generally relates to computer software for business management and, more particularly, to a computer implemented method for generating sensitivity information about average lost sales and inventory levels of a lost-sale (R,s,S) inventory system for what-if analysis and optimization of the decision variables s and S.
2. Background Description
The system under consideration manages the inventory level of an item where once every period or at recurring intervals, the inventory level is reviewed and, if necessary, purchase orders are placed to replenish depleted inventory, in accordance with a pre-specified decision rule. An (s,S) inventory policy is one such decision rule that specifies that an order be placed when the level of inventory on hand plus on order falls below the level s (a specified number), and the amount of order be the difference between S (another specified number) and the present level of inventory on hand plus on order; i.e., every time the inventory position (which refers to the sum of inventory on hand plus on order) falls below s, an order is placed to bring it up to S.
(s,S) policies are of great practical and theoretical interest, and much effort has gone into the determination of the appropriate values of s and S to optimize system performance measures and to obtain sensitivity information in this regard. The determination of these values becomes exceedingly complicated in the general case due to a number of factors. Specifically, the inventory system may be of the back order or lost sale type (depending on whether requests are backlogged or refused when there is no inventory on hand), and the demand distribution to which the system is subjected may vary over time. The term "demand distribution", as used in this description, means the statistics of the consumer demand per unit time period, in terms of known approximation forms for, and/or hypothetical models based on, probability density and distribution functions characterizing observed sales events or hypothetical sales statistics, respectively. The only requirement for the selected demand distributions are that they be unambiguous and that they provide sufficient information to generate values of simulated demand over the time horizon under consideration.
In such cases of determining appropriate values of s and S to optimize system performance measures and to obtain sensitivity information, simulation is a useful tool to obtain information about the expected performance. Due to the requirement that several replications of the simulation have to be done to obtain meaningful estimates of performance, and the fact that a typical manufacturer/retailer has thousands of items in inventory, the use of simulation to do sensitivity analysis to changes in s and S values becomes an extremely time consuming task. This has made undesirable and in some cases precluded the use of simulation to do performance analysis and optimization.
To address this problem, investigations into obtaining the sample path derivative of performance measures with respect to s and S have been conducted for the back order case with stationary demands. See M. C. Fu, "Sample path derivatives for (s,S) inventory systems", Operations Research, Vol. 42, No. 2, pp. 351-364 (1994). Extensions to address stochastic lead times are presented in M. C. Fu and J-Q Hu, "(s,S) inventory systems with random lead times", Probability in the Engineering and Informational Sciences, Vol. 8, pp. 355-376 (1994). The use of Perturbation Analysis to obtain sensitivity information on inventory levels for base stock multi-echelon systems in discussed in P. Glasserman and S. Taylor, "Sensitivity analysis for base-stock levels in multiechelon production-inventory systems", Management Science, Vol. 41, No. 2, pp. 263-281 (1995). However, none of the methods in the surveyed literature address either the lost sales case or the case with non-stationary demands.